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Simplifying 180 = 90(2x + -3) * x Reorder the terms: 180 = 90(-3 + 2x) * x Reorder the terms for easier multiplication: 180 = 90x(-3 + 2x) 180 = (-3 * 90x + 2x * 90x) 180 = (-270x + 180x2) Solving 180 = -270x + 180x2 Solving for variable 'x'. Reorder the terms: 180 + 270x + -180x2 = -270x + 270x + 180x2 + -180x2 Combine like terms: -270x + 270x = 0 180 + 270x + -180x2 = 0 + 180x2 + -180x2 180 + 270x + -180x2 = 180x2 + -180x2 Combine like terms: 180x2 + -180x2 = 0 180 + 270x + -180x2 = 0 Factor out the Greatest Common Factor (GCF), '90'. 90(2 + 3x + -2x2) = 0 Factor a trinomial. 90((2 + -1x)(1 + 2x)) = 0 Ignore the factor 90.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {2, -0.5}
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